isobaric modulus of elasticity is

Options

A. `oo`
B. zero
C. 1
D. `(C_(p))/(C_(v))`

Explanation

To find the isobaric modulus of elasticity, we need to understand the definitions and principles involved. Here’s a step-by-step solution:

### Step 1: Understand Isobaric Process
- An isobaric process is one in which the pressure remains constant throughout the process. This means that any changes occurring in the system do not involve a change in pressure.

**Hint:** Remember that "isobaric" directly relates to constant pressure conditions.

### Step 2: Define Modulus of Elasticity
- The modulus of elasticity (E or Y) is defined as the ratio of stress to strain. It quantifies how much a material deforms under stress. There are different types of modulus of elasticity:
- Longitudinal modulus (for longitudinal strain)
- Bulk modulus (for volumetric strain)
- Shear modulus (for shear strain)

**Hint:** Modulus of elasticity is a measure of a material's stiffness.

### Step 3: Identify the Relevant Modulus for Isobaric Process
- In the context of an isobaric process, we are interested in the bulk modulus of elasticity (K), which relates to changes in volume under constant pressure.

**Hint:** Focus on the bulk modulus when dealing with volume changes.

### Step 4: Write the Formula for Bulk Modulus
- The bulk modulus (K) is defined as:
\[ K = -\frac{dP}{\frac{dV}{V}} \]
where \(dP\) is the change in pressure and \(\frac{dV}{V}\) is the volumetric strain (change in volume divided by original volume).

**Hint:** The negative sign indicates that an increase in pressure leads to a decrease in volume.

### Step 5: Analyze the Isobaric Condition
- Since the process is isobaric, the change in pressure (\(dP\)) is zero:
\[ dP = 0 \]

**Hint:** Recognize that if pressure does not change, the bulk modulus will be affected.

### Step 6: Substitute into the Bulk Modulus Formula
- Substituting \(dP = 0\) into the bulk modulus formula gives:
\[ K = -\frac{0}{\frac{dV}{V}} = 0 \]

**Hint:** A zero change in pressure leads to a zero value for the bulk modulus.

### Conclusion
- Therefore, the isobaric modulus of elasticity is 0.

**Final Answer:** The isobaric modulus of elasticity is 0.